Warm up
Write the exponential function for each table.
x
0
1
2
y
1
x
y
0
2
1
3
2
5
3
9
5
25
Arithmetic & Geometric
Sequences
Recursive
Sequences are a list of numbers
that form a pattern. What do you
notice about the sequences below
and how to they relate to what
you have learned so far in this
unit?
•-3,0,3,6,9…
•1,4,16,64…
Recursive Formula
a formula used to find
the next term of a
sequence when the
previous term is known
Recursive Formula for
Arithmetic Sequence
an  an1  d
a1  ____
Recursive Formula for
Geometric Sequence
an  an1  r 
a1  _____
Find the next term and write the
recursive rule.
x
1
2
3
4
n
y
3
13
23
33
next term: 43
d  10
an  an1  d
a1  3, an  an1  10
Find the next term and write the
recursive rule.
x
1
2
3
4
n
y
16
40
100
250
next term: 625
40
r
 2.5
16
an  an1  r 
a1  16, an  2.5an1
Find the next term and write the
recursive rule.
x
1
2
3
4
n
y
2
14
98
686
next term: 4802
14
r
7
2
an  an1  r 
a1  2, an  7an1
Explicit Rule
The explicit rule is used to
find any term in the
sequence not just the next
one
Explicit Rule for
Arithmetic Sequences
an  a1  d (n  1)
Explicit Rule for
Geometric Sequences
an  a1  r 
n1
Find the next term and write the
explicit rule.
x
1
2
3
4
n
y
19
13
7
1
d  6
next term: -5
an  19  6(n  1)
Write the explicit rule and the
recursive rule.
a1 = 15 and d = 5
Explicit : an  a1   n  1 d Recursive : an  an1  d
an  15   n  1 5
an  15  5n  5
function rule:
an  5n  10
a1  15, an  an1  5
Write the explicit rule and the
recursive rule.
a1 = 4 and r = 0.2
Explicit : an  a1  r 
an  4  0.2 
n1
n1
Recursive : an  an1  r 
a1  4, an  (0.2)an1
Practice Worksheet
Sequences Practice Worksheet
#26